Newton's Views on Space, Time, and Motion

Isaac Newton founded classical mechanics on the view that
space is distinct from body and that time
passes uniformly without regard to whether anything happens
in the world. For this reason he spoke of absolute space and
absolute time, so as to distinguish these entities from the
various ways by which we measure them (which he called relative
spaces and relative times). From antiquity into the
eighteenth century, contrary views which denied that space and time
are real entities maintained that the world is necessarily a material
plenum. Concerning space, they held that the idea of empty space is a
conceptual impossibility. Space is nothing but an abstraction we use
to compare different arrangements of the bodies constituting the
plenum. Concerning time, they insisted, there can be no lapse of time
without change occurring somewhere. Time is merely a measure of
cycles of change within the world.

Associated with these issues about the ontological status of space
and time was the question of the nature of true motion. Newton defined
the true motion of a body to be its motion through absolute
space. Those who, before or shortly after Newton, rejected the reality
of space, did not necessarily deny that there is a fact of the matter
as to the state of true motion of any given body. They thought rather
that the concept of true motion could be analyzed in terms of the
specifics of the relative motions or the causes thereof. The
difficulty (or, as Newton alleged, the impossibility) of so doing
constituted for Newton a strong argument for the existence of absolute
space.

In recent literature, Newton's theses regarding the ontology of space
and time have come to be called substantivalism in contrast
to relationism. It should be emphasized, though, that Newton
did not regard space and time as genuine substances (as are,
paradigmatically, bodies and minds), but rather as real entities with
their own manner of existence as necessitated by God's existence (more
specifically, his omnipresence and eternality).

Today, Newton is best known as a physicist whose greatest single
contribution was the formulation of classical mechanics and
gravitational theory as set out in his Philosophae Naturalis
Principia Mathematica (Mathematical Principles of Natural
Philosophy), first published in 1687, and now usually referred to
simply as “Newton's Principia”. Newton's views on
space, time, and motion not only provided the kinematical basis for
this monumental work and thus for the whole of classical physics up
until the early twentieth century, but also played an integral role in
Newton's general system of philosophy and theology (largely developed
prior to the Principia). Because Newton never drafted a
treatise on, or even a digest of, this general system, his stature as
one of the great philosophers of the seventeenth century, indeed, of
all time, is no longer widely appreciated.

A “Scholium” at the beginning of the Principia,
inserted between the “Definitions” and the “Laws of
Motion”, lays out Newton's views on time, space, place, and
motion. He begins by saying that, since in common life these
quantities are conceived of in terms of their relations to sensible bodies, it is
incumbent to distinguish between, on the one hand, the relative,
apparent, common conception of them, and, on the other, the absolute,
true, mathematical quantities themselves. To paraphrase:

Absolute, true, and mathematical time, from its
own nature, passes equably without relation to anything external, and
thus without reference to any change or way of measuring of time
(e.g., the hour, day, month, or year).

Absolute, true, and mathematical space remains
similar and immovable without relation to anything external. (The
specific meaning of this will become clearer below from the way it
contrasts with Descartes' concept of space.) Relative spaces are
measures of absolute space defined with reference to some system of
bodies or another, and thus a relative space may, and likely will, be
in motion.

The place of a body is the space which it
occupies, and may be absolute or relative according to whether the
space is absolute or relative.

Absolute motion is the translation of a body from
one absolute place to another; relative motion the translation from
one relative place to another.

Newton devotes the bulk of the Scholium to arguing that the
distinction between the true quantities and their relative measures is
necessary and justified.

It is evident from these characterizations that, according to Newton:

space is something distinct from body and exists independently of
the existence of bodies,

there is a fact of the matter whether a given body moves and what
its true quantity of motion is, and

the true motion of a body does not consist of, or cannot be
defined in terms of, its motion relative to other bodies.

The first of these theses was a point of major contention in
17th-century natural philosophy and one assailed by Newton's critics
such as Leibniz, Huygens, and Berkeley. The second was not in
general dispute. Descartes, Leibniz, and Berkeley all believed that,
to put it in somewhat scholastic terms, the predicate ‘x is
in true motion’ is a complete predicate in the sense that it holds or
fails to hold for any given body. (Huygens, at least in his
post-Principia views, constitutes a special case.) Thus, for
those who denied the first thesis, it was necessary to secure a
definition, or an analysis, of what it means for a body be in true
motion (and what determines the quantity of that motion), so as to be
as adequate to the facts as Newton's characterization of true
motion. The figures mentioned above all deemed that motion relative to
other bodies is a necessary condition for true motion,
although not, by itself, a sufficient condition.

Over the course of years, the consensus in the 17th and early 18th
Centuries on thesis (2) was lost sight of, and it became common to
characterize Newton's opponents as denying that there is a
fact of the matter as to whether a body is in true motion and
maintaining instead that all motion is merely relative
motion. Thus, modern readers expect that Newton's Scholium on
space, time, and motion should be read as arguing not only thesis (1)
above, but also thesis (2), that all motion is not merely relative
motion, but that some motions are true and absolute. Newton's
arguments concerning motion, however, are designed to show, not that
true motion is distinct from merely relative motion (which is granted
by all), but rather that the only feasible analysis of true motion
requires reference to absolute places, and thus the existence of
absolute space.

In particular it has been assumed that Newton's so-called “rotating
bucket experiment”, together with the later example of a pair of
globes connected by a chord and revolving about their center of
gravity, is supposed to argue, or provide evidence for, the existence
of true, or absolute, motion. Not only is this false, but the two
cases have distinct purposes in the framework of the Scholium. The
rotating bucket experiment is the last of five arguments from the
“properties, causes, and effects of motion” designed to show
cumulatively that an adequate analysis of true motion must involve
reference to absolute space. In contrast, the example of the revolving
globes is intended to illustrate how it is that, despite the fact that
absolute space is invisible to the senses, it is nonetheless possible
to infer the quantity of absolute motion of individual bodies in
various cases.

The most important question shaping 17th-century views on the nature
of space, time and motion is whether or not a true void or vacuum is
possible, i.e., a place devoid of body of any sort (including rarified
substances such as air). Ancient atomism, dating back at least to the
pre-Socratic philosopher Democritus (5th century, B. C.), held that
not only is such possible, but in fact actually exists among the
interstices of the smallest, indivisible parts of matter and extends
without bound infinitely. Following Plato, Aristotle rejected the
possibility of a void, claiming that, by definition, a void is
nothing, and what is nothing cannot exist.

According to Aristotle, the universe is a material plenum, finite in
extent, bounded by the outermost sphere of the fixed stars. Beyond
that there is no void, i.e., empty places, since, as Aristotle defines
‘place’, the place of something is the outermost of “the
innermost motionless boundary of what contains it.” Hence, since there
are no boundaries outside the outermost celestial sphere, there are no
places or space outside of it.

Time, according to Aristotle, is just the measure of motion, where by
‘motion’ he means change of any sort, including
qualitative change. In order to define the uniformity of time, that
is, the notion of equal intervals of time, Aristotle was guided by
astronomical practice, which in antiquity provided the most practical and accurate measures of time. He identified uniform motion with the rate of motion of
the fixed stars, a choice for which he found a dynamical justification
in his celestial physics.

“Local” motion is but one species of motion, viz., change of
place. Motion, in general, he defined as the actualization of
potentiality, a notion commonly held in the 17th century to be so
obscure as to be either useless or meaningless. However, as far as
local motion is concerned, there is no difficulty as to what
constitutes the true or absolute motion of a body in a finite
geocentric universe. Indeed, elementary substances in the sub-lunar
realm (earth, air, fire, and water) move of their own accord either up
or down, i.e., toward the center or away from the center by their very
nature. The celestial realm, beginning with the orbit of the moon,
consists of an interlocking network of celestial spheres composed of a
fifth element (aether), which by its nature is disposed to circular
motion about the center of the of universe (i.e., the center of the
earth). If the motion of this substance is taken to be the measure of
time, the celestial spheres necessarily rotate uniformly. Since the
net motion of an embedded sphere is the sum of its natural motion
superimposed on the natural motions of the spheres in which it is
embedded, and since the axes of rotation are in general set at
slightly different angles in order to account for why the sun does not
move on the celestial equator and the planets and the moon do not move
strictly on the ecliptic (i.e., the path of the sun against the fixed
stars), the motions of the moon, planets, and even the sun are not
necessarily uniform. However, since the sphere of the fixed stars is
embedded in no other celestial sphere in motion, the motion of the
fixed stars is de facto the measure of all motion.

The motions spoken of so far are all natural motions of the
substances in questions, motions induced by the body being the very
substance that it is. In contrast, other motions, in which the cause
of the motion is external rather that internal to the body, Aristotle
subsumed under the concept of violent motion. Violent motion
required for its continuation the constant application of an external
cause.

Although Aristotle's views dominated medieval scholasticism, there
occurred a renewed interest in atomism in the early 17th
Century. Apart from general factors such as the Renaissance, Humanism,
and the Reformation, specific innovations of the 16th Century made it
attractive. Although Copernicus' introduction of a helio-static system
was motivated by a strict adherence to Aristotle's dynamics of
celestial spheres, it brought into question his terrestial
physics. Galileo's telescopic observations of the surface of the moon and
his discovery of moons orbiting about Jupiter brought into question
the very distinction between the terrestial and the
celestial. Moreover, the visibility of an abundance of new stars,
apparently without end, suggested that the universe may in fact be
without bound.

An important representative of the revival of atomism and its
concomitant views concerning the void is Walter Charleton's
Physiologia Epicuro-Gassendo-Charltoniana: Or a Fabrick of Science
Natural, upon the Hypothesis of Atoms, “Founded by Epicurus, Repaired
by Petrus Gassendus, Augmented by Walter Charleton”, which
appeared in English in 1654, twelve years after Newton's birth. It is
a text with which Newton became familiar as an undergraduate, and some
of the core theses concerning time and space later put forth in the
Principia and various unpublished manuscripts in Newton's hand can be
found in Charleton. These include:

that time and space are real entities even though they fit neither
of the traditional categories of substance or accident (i.e., property
of a substance),

that time “flow[s] on eternally in the same calm and equal tenor,”
while the motion of all bodies is subject to “acceleration,
retardation, or suspension”,

that time is distinct from any measure of it, e.g., celestial
motion or the solar day,

that space is “absolutely immoveable” and incorporeal,

that bodies, or “Corporeal Dimensions” are everywhere “Coexistent
and Compatient” with the “Dimensions” of the parts of space they
occupy,

that space distinct from body existed before God created the world
and that God's omnipresence is his literal presence everywhere, and

that motion is the translation or migration of body from one
place, as an immovable part of space, to another.

Charleton's arguments for his views concerning time have much the
same tenor as those given by Newton in the Principia. In
marked contrast, though, those for empty, immense, and immutable space
are quite different. Charleton appeals to the explanation of such
phenomena as rarefaction and condensation, the differences in “degrees
of Gravity” of bodies, and the numerous ways in which bodies can
interpenetrate at the micro-level in terms of solubility, absorption,
calefaction, and diverse chemical reactions. However, Charleton does
not introduce the terminology of “relative” time, “relative” spaces,
or “relative” places, and nowhere raises concerns regarding true
(absolute) motion versus merely relative motion. Oddly enough,
although Charleton occasionlly mentions and criticizes Descartes with
regard to other matters, no note of the fact is made that Descartes, a
decade earlier, had proposed explanations, in detail or in outline,
for just these sorts phenomena according to a system of nature in
which the world is completely filled with matter and in which space
distinct from body cannot exist. Descartes, it can be justly said, is
the founder of the other main school of the “mechancal philosophy” of
the 17th Century, which stood in direct opposition to atomism on the
issue of the possibility of a vacuum and which adapted the
Aristotelian doctrines on the nature of time, space, and motion to the
new world view.

Although avowedly anti-Aristotelian in many regards, particularly on
the view, shared with atomists, that all qualitative change on the
macroscopic scale is reducible to the rearrangement and/or motion of
matter on the microscopic scale, it was Descartes' ambition to carry
out this program by retaining what is essentially Aristotle's notion of
Prime Matter. The pure elements (earth, air, fire, and water) of
Aristotle's physics could mutate into one another by alteration of the
fundamental qualities definitive of them. These were the four haptic
qualities of hot, cold, wet, and dry. Because of this, there had to be
something distinguishable, at least in thought, from qualities that
persist during elemental alteration. This quality-less substratum is
what Aristotle referred to simply as matter, or as it is often called,
Prime Matter, in order to avoid confusion with the macroscopically
identifiable, quality-laden, homogenous portions of everyday
objects. Unlike atomists, who attributed at least the quality of
hardness (impenetrability) to the ultimate particles of matter,
Descartes argued that matter, or synonymously, body [corpus] has no
qualities whatsoever, but only quantity, i.e., extension. In other
words, body and extension are literally one and the same [res
extensa]. An immediate corollary is that there can be no vacuum, for
that would require an extended region devoid of body --- a manifest
contradiction. The task, then, was to show how all apparent qualities
can be explained in terms of the infinite divisibility and
rearrangement of extension with respect to itself. The task was grand
indeed, for its goal was to develop a unified celestial and
terrestrial physics that could account equally for the ductility of
metals, magnetic attraction, the tides, the mechanism of gravity, the
motion of the planets, the appearance and disappearance of comets, and
the birth and death of stars (supernovae).

Descartes published his system of the world in 1644 as the
Principles of Philosophy (Principia
Philosophae). Part II of the Principles lays out the
thesis of the identity of space (extension) and matter, develops a
definition of motion in the “true, or philosophical sense”, and sets
out the fundamental dynamical laws of his system. Motion, according to
“the truth of the matter”, is defined to be “the translation of one
part of matter, or one body, from the vicinity of those bodies, which
are immediately contiguous to it and are viewed as if at rest, to the
vicinity of others.” In consequence, Descartes points out, each body
has a single motion proper to it (in contrast to the numerous relative
motions that can be ascribed to it depending on which other bodies are
selected in order to determine its place). It is this single proper
motion that figures in his laws of motion. Of particular importance
for Descartes' entire system, is that a body in circular motion has an
endeavor [conatus] to recede from the center of rotation.

This fact, together with Descartes' contention that a body also
participates in the motion of a body of which it is a part, makes it
difficult to reconcile Descartes' system of the world with his
definition of proper motion. Newton concluded that the doctrine is in
fact self-refuting and that, where Descartes needed to, he had
surreptitiously helped himself to a notion of space independent of
body, particularly in order to assign the desired degree of
centrifugal conatus to the planets and their satellites as
they are swept about by celestial vortices of “subtle” matter.

The untitled and unfinished manuscript which begins “De Gravitatione
et aequipondio fluidorum et solidorum …”, written perhaps a decade
or more before the Principia, consists for the most part of
an extensive and scathing critique of Descartes' doctrine of
motion. The document, published for the first time in (Hall and Hall,
1962), is well worth the study for a glimpse at the development of
Newton's thinking at a relatively young age. It manifestly embraces
the doctrines of space and time later codified in the
Principia. Notable, as well, is that each of the five
arguments from the properties, causes and effects of motion advanced
in the Scholium has a clearly identifiable antecedent in De
Gravitatione. (See Rynasiewicz 1995 for details.) This makes it
clear the extent to which the Scholium is concerned to argue
specifically against the Cartesian system (as pointed out by Stein
1967), which Newton perceived to be the only other viable contender at
the time.

The Scholium has a clearly discernible structure. Four paragraphs
marked by Roman numerals I–IV follow the opening paragraph, giving
Newton's characterizations of time, space, place and motion,
respectively, as summarized in the third paragraph of Section 1
above. If we were to extend Newton's enumeration to the remaining
paragraphs, then paragraphs V–XII constitute a sustained defense of
the distinctions as characterized in I–IV. Paragraph XIII then
states the general conclusion that the relative quantities are
genuinely distinct from the respective absolute quantities and makes
comments on the semantic issue of the meanings of these terms in the
Bible. There follows one remaining, and quite extensive paragraph
[XIV], which takes up the question how in practice one can ascertain
the true motions of bodies and concludes: “But how we are to obtain
the true motions from their causes, effects and apparent differences,
and vice-versa, will be explained at length in the treatise that
follows. For that is the end to which I composed it.”

In what follows, links have been inserted to the text of the Scholium
according to the extended enumeration suggested above. Clicking on a
link will open a new window in such a way that the reader can navigate
back and forth between a given paragraph of the text and the
commentary elucidating that paragraph.

Paragraph
V
appeals to the fact that astronomy distinguishes between absolute and
relative time in its use of the so-called equation of time. This
serves to correct for inequalities in the commonly adopted standard of
time, the solar day, which most people mistakenly believe
to be uniform. The solar day, defined as the period of time it takes
the sun to return to zenith, varies by as much as 20 minutes over the
course of a year. The standard of correction in the equation of time
used in Ptolemaic astronomy was based upon the assumption that the
sidereal day—the period of time it takes a fixed star to return
to zenith—is constant, because the celestial sphere on which
the fixed stars are located should not be assumed to speed up and slow
down. With the demise of the Ptolemaic system and Aristotelian
cosmology, this rationale was no longer compelling, and at least some
astronomers, most notably Kepler, called into doubt whether the rate of
rotation of the earth remained constant over the course of the
year. (Kepler considered that its rotation would be faster when closer
to the sun due to an excitatory effect of the sun.) Thus, the issue of
the correct measure of time occupied considerable attention in 17th
Century astronomy, especially because the ability to measure the rate
of rotation of the earth is equivalent to the problem of determining
longitude, which, for sea-faring nations, was critical for navigation
(and hence military and economic dominance). Huygens' pendulum clock
provided the first terrestrial candidate for a decently accurate
measure of uniform time. Newton mentions this, as well as the eclipses
of the moons of Jupiter, an alternative method based on Kepler's
period law.

The invocation of the need for an equation of time in astronomy is
not just an appeal to a well entrenched scientific practice. In the
course of his discussion, Newton explains why he thinks the need is
justified. Although he will argue in Book
III of the Principia that the diurnal rotation of the earth
is uniform, this is a contingent fact. It could have been otherwise.
Indeed, it could have been that there are
no uniform motions to serve as accurate measures of
time. The reason is that all motion is subject to being accelerated or
retarded (by the application of external forces). In contrast,
absolute time (which is nothing other than duration or the
perseverance of the existence of things) remains the same, whether the
motions be be swift, slow, or null.

Paragraph
VI
defends
the thesis of the immobility of (absolute) space, which against the
backdrop of Descartes, clearly means that the parts of space, just as
the parts of time, do not change their relation with respect to one
another. Newton argues that the parts of space are their own places,
and for a place to be moved out of itself is absurd. A more expansive
antecedent of this argument occurs in De Gravitatione,
applied specifically to time: if yesterday and tomorrow were to
interchange their temporal relations with respect to the remainder of
time, then yesterday would become today, and today yesterday. Thus,
Newton held an interestingly holistic identity criterion for the parts
of space and time.

Newton devotes five full paragraphs to justifying his
characterization of the distinction between absolute and relative
motion. The first three present arguments from properties of absolute
motion and rest, the next presents an argument from their causes, and
the final an argument from their effects. The force of these has
confused modern commentators for a combination of reasons which,
historically, are difficult to untangle. Since only those not already
prejudiced by those commentaries, directly or indirectly, will find
what follows unusual, it is best to defer an autopsy of those reasons
until Section 6, after an exposition of the arguments.

Suffice it to say for the moment that it is a common misunderstanding
that in these arguments Newton intends to develop empirical
criteria for distinguishing cases of absolute motion from merely
apparent motion and thereby to disprove the thesis that all motion is
merely relative motion. To the contrary,
the arguments take as their point of departure the assumption, common
to Cartesian and Aristotelian philosophy, that each body has a unique
state of true motion (or rest). Throughout the arguments, the terms
‘true motion’ and ‘absolute motion’ are
treated synonymously. At issue is whether true motion (and rest) can
be reduced to some special instance of relative motion (or rest) with
respect to other bodies. In announcing at the outset of these
arguments that “absolute and relative rest and motion are
distinguished by by their properties, causes, and effects”, Newton
indicates his intent to show that they cannot, at least if true motion
and rest are to have those features we generally associate, or ought
to associate, with them.

Property: Bodies that are truly at rest are at rest
with respect to one another.

Conclusion: True rest cannot be defined simply in
terms of position relative to other bodies in the local
vicinity.

Reasoning: Suppose there were a body somewhere in
the universe absolutely at rest, say far away, in the region of the
fixed stars, or even farther. (Whether or not that body might ever be
observed doesn't enter into what follows.) Clearly it is impossible to
know just from considering the positions of bodies in our region
relative to one another whether any of these latter bodies maintains a
fixed position with respect to that hypothetical distant body. To
amplify, let B be one of the local bodies, C the relative
configuration over time of the set of local bodies, and A the far
distant body at absolute rest. The specification of C alone fails to
establish the position of B relative to A over time. In particular, C
fails to establish whether B is relatively at rest with respect A,
which, by the property stated above, is a necessary condition for B to
be absolutely at rest. Hence, specification of the local configuration
C underdetermines whether or not B is at absolute rest. Thus the
conclusion: it is impossible to define what it is for a body such as B
to be at absolute rest [i.e., to give necessary and sufficient
conditions for when it is that B is at rest] simply in terms of how B
fits into the local configuration C.

Property: If a part of a body maintains a fixed
position with respect to the body as a whole, then it participates in
the motion of the whole body.

Conclusion: True and absolute motion cannot be
defined as a translation from the vicinity of (the immediately
surrounding) bodies, viewing the latter as if they were at rest.

Reasoning: Newton first introduces two
considerations that can be taken either to support, or to illustrate,
or to amplify upon the import of the stated property. The first is
that if a part of a rotating body is at rest relative to the body as a
whole, it endeavors to recede from the axis of rotation. The second is
that the impetus of a body to move forward arises from the combination
of the impetus of its parts.

From the property it follows that if those bodies surrounding a given
body move (either rotationally or progressively forward as a fixed
configuration) while the surrounded body is at rest relative to the
surrounding ones, then the surrounded body partakes in the (true)
motion of the group of surrounding bodies. Hence, if the surrounding
bodies move truly, then so does the surrounded body. But according to
the (Cartesian) definition of motion—which identifies the true
motion of a body with its transference from the vicinity of
immediately surrounding bodies, regarding the surrounding bodies to be
as though they are at rest—it would have to be said (wrongly)
that the surrounded body is truly at rest. Hence that definition is
untenable.

Property: Anything put in a moving place moves along
with that place, and hence a body participates in the motion of its
place when it moves [relatively] away from that place.

Conclusion: The complete and absolute motion of a
body cannot be defined except by means of stationary places.

Reasoning: From the property, the [relative] motion
of a body out of a given place is only part of the motion of the body
if the place in question is itself in motion. The complete and true
motion of the body consists of its motion relative to the moving place
added vectorially to whatever motion the place may have. Should the
place be moving relative to a place which is in turn moving, then the
motion of that place must be added, and so on. Barring infinite
regress, the sum must terminate with a motion relative to a stationary
place.

Addended Argument: After deriving this conclusion,
Newton amplifies upon the consequences. The only places that are
stationary are all of those that that stay in fixed positions with
respect to one another from infinity to infinity, and since these
always remain stationary, they make up what Newton calls immobile
absolute space.

Causes: the forces impressed upon bodies. The major
premise is that application of a [non-zero net] force on a body is
both a necessary and sufficient condition for either generating or
altering its true motion. More specifically:

(A) Impressed force is a necessary condition for generating or
altering true motion (but not, as remains to be shown, merely relative
motion).

(B) Application of a [non-zero net] force is a sufficient condition
for the generation or alteration of true motion (but not, as will be
shown subsequently, merely relative motion).

Conclusion: The true motion of an individual body
cannot be defined as any particular sub-instance of its motion
relative to other bodies.

Reasoning: Newton seeks to establish that
application of a positive net force to a body is neither a necessary
not a sufficient condition for the generation of motion relative to
other bodies. The two lines of reasoning are given separately, call
them ‘Prong A’ and ‘Prong B’, respectively.

Prong A: To be established is that, although an impressed
force is necessary for the generation or alteration of true motion in
a body, it is not necessary for the generation of motion relative to
other bodies. The reasoning is quite simple: pick a given body and
merely apply the same [accelerative] force to all other bodies in
question. These other bodies will then remain in the same relative
configuration with respect to one another, but a relative motion with
respect to the original body [to which no force has been applied] will
either be generated or altered.

Prong B: To be established is that, although an impressed
force is sufficient for the generation or alteration of true motion in
a body, it is not sufficient for the generation of motion relative to
other bodies. Again, the line of reasoning is quite
straightforward. Consider an arbitrarily given body amongst a system
of bodies and simply apply the same [accelerative] force to all bodies
in question. Then, despite the fact that a force has been impressed
upon the originally given body, there is neither generation nor
alteration of relative motion with respect to the remaining bodies.

Effects: the forces of receding from the axis of
rotational motion [centrifugal endeavor]. The major premise is that
the centrifugal endeavor of bodies [or parts of bodies] to recede from
the axis of rotation is directly proportional to the quantity of the
true circular motion.

Conclusion: True rotational motion cannot be defined
as relative rotation with respect to the surrounding bodies.

Reasoning: The line of reasoning is in fact parallel
to the preceding argument from causes, although this may not be
completely perspicuous due to the fact that the correlates of the two
prongs above are here stages of a single on-going experimental
situation, the so-called “rotating bucket” experiment, which, Newton
intimates, he actually performed. In order to set up this experiment,
one suspends a bucket using a long cord and by turning the bucket
repeatedly, winds up the cord until it is strongly twisted, then fills
the bucket with water. During the course of the experiment, the degree
to which the water tries to climb up the sides of the bucket is used
as a measure of its centrifugal endeavor to recede from the
center. Newton uses the experiment to establish that centrifugal
endeavor is neither a necessary condition nor a sufficient condition
for the existence of relative circular motion [of the water] with
respect to its surroundings [the bucket].

Stage 1: When the bucket is first released, it rotates
rapidly with respect to the rest frame of the experimenter while the
water remains at rest with respect to the experimenter. In other
words, there is rapid relative motion of the water with respect to the
bucket. However, the surface of the water remains flat, indicating
that it has no tendency to recede from the axis of relative
rotation. Thus, the existence of centrifugal endeavor in the parts of
a body is not a necessary condition for the body to be rotating
relative to its surroundings. That is, such relative rotation with
respect to immediately adjacent bodies need not produce any
centrifugal endeavor in the parts of the body to recede from the axis
of relative rotation.

In the further course of the experiment, as the bucket continues to
rotate, the water gradually begins to rotate with it, and as it does
so, begins to climb up the sides of the bucket. Eventually, according
to Newton, the water acquires the same rotation of the bucket relative
to the lab frame, at which point we have the following situation.

Stage 2: The water and the bucket are at relative rest, yet
the water has achieved its highest ascent up the sides of the bucket,
indicating a maximum centrifugal endeavor to recede from the axis of
common rotation. Hence, the existence of centrifugal endeavor is not a
sufficient condition for the presence of relative circular motion
between a body and its surroundings, i.e., if a body, or rather its
parts, have a centrifugal endeavor to recede from a central axis, it
does not follow that there is a relative circular motion of the body
with respect to its immediate surroundings.

Astrophysical Application. After deriving the
conclusion, Newton uses the premises of the first two arguments from
properties, together with the premise of the argument from effects, to
critique the vortex theory of planetary motion. According to that
theory, each of the planets (and most notably the earth) is relatively
at rest with respect to the “subtle” matter of the celestial vortex of
our own sun. Hence, according to Descartes' own definition of true
motion (as well as his explicit insistence), they have no true
motion. However, it is manifest that they do not maintain fixed
positions with respect to one another. So, according to the property
invoked in the first argument, they cannot [all] be truly at
rest. Moreover, from the property invoked in the second argument, they
partake in the circular motion of the solar vortex [assuming that
motion to be true motion, as Descartes implicitly assumed]. Finally,
because they would accordingly participate in the true circular motion
of this hypothetical vortex, they should have an endeavor to recede
from the axis of its rotation.

This completes the sequence of arguments from the properties, causes,
and effects of motion. The next paragraph
[XIII]
states the cumulative conclusions of the arguments marshalled
beginning with the arguments for absolute time in paragraph V: “Hence
relative quantities are not the quantities themselves, whose names
they bear, but are only sensible measures of them (either accurate or
inaccurate), which are commonly used in place of the quantities they
measure.” Having made his case, Newton comments on the ordinary
language meaning of the terms for these quantities
in order to address contemporary issues of dogma
and heresy.

Galileo's condemnation by the Catholic Church for asserting that the
earth is in motion was still recent history at the time Newton
composed the Principia. Descartes, who lived in reach of
Papal authority and feared similar fate, had found a clever way of
espousing Copernicanism without falling prey to accusation of
heresy. According to his definition of motion “properly speaking”, he
contends, the earth is truly at rest.

In Newton's system of the world as set out in Book III of the
Principia, the earth patently moves absolutely. In
anticipation, Newton indicates how to reconcile this with scripture by
observing that, if usage determines the meanings of words, then in
ordinary discourse (including the Bible) the terms ‘time’,
‘space’, ‘place’, and ‘motion‘ are
properly understood to signify the relative quantities; only in
specialized and mathematical contexts do they denote the absolute
quantities. (Keep in mind Newton's title, The
Mathematical Principles of Natural Philosophy.)
He proceeds to chastise Descartes on two counts, first for doing
violence to the scriptures by taking them to refer to the absolute
quantities, and second, for confusing the true quantities with their
relative measures.

Having argued his case that true motion consists in motion with
respect to absolute space, and thus having dealt to his satisfaction
with the metaphysics of motion, Newton turns in the final
paragraph of the Scholium to epistemological strategies
available on his account. On an Aristotelian or Cartesian account, one
can directly observe the allegedly absolute motion of a body if both
it and its immediate surroundings are visible. In contrast, because
the parts of absolute space are not directly accessible to the senses,
it is very difficult, Newton confesses, to ascertain the true motion of
individual bodies and to discriminate them in practice from the
apparent motions. “Nevertheless,” he remarks in a rare moment of wit,
“the situation is not entirely desperate.” Evidence is available in
part from apparent motions, which are the differences of true motions,
and in part from the forces, which are the causes and effects of true
motions.

Newton illustrates with an example. Imagine a pair of globes,
connected by a cord, revolving about their common center of
gravity. The endeavor of the globes to recede from the axis of motion
is revealed by the tension in the cord, from which the quantity of
circular motion can be estimated. Furthermore, whether the direction of
their revolution is clockwise or counterclockwise can be detected by
applying forces to opposite faces of the globes to see whether the
tension in the cord increases or decreases. All this can be done in
empty space where no other bodies are present to serve as points of
reference.

Suppose now that, in addition to the globes, there is second system
of bodies maintaining fixed positions with respect to one another (for
example, the fixed stars). If the two systems are in a state of
relative rotation, one cannot gauge from just the relative rotation,
which, if either, is at rest. However, from the tension in the cord
connecting globes, one can establish whether the relative rotation is
due entirely to the absolute rotation of the system of
globes. Supposing so, the second system of bodies can then be
exploited to provide an alternative technique for determining whether
the globes revolve in a clockwise or counterclockwise
direction—one simply consults the direction of rotation relative to
the stationary system.

At this point Newton cuts off the Scholium, explaining that the whole
point of having written the treatise to follow is to show how to infer
the true motions from their causes, effects, and apparent differences,
and conversely the causes and effects from either the true or the
apparent motions.

As remarked in Section 5.3 above, the purpose of the arguments from
properties, causes, and effects has been widely misunderstood in both
the historical and philosophical literature, and as a consequence, so
too the relation of these to the example of the revolving globes in
the final paragraph. Some diagnosis as to why may help those readers
already steeped in tradition to overcome certain prejudices they bring
to the Scholium and may also serve to further illuminate the framework
in which Newton and his contemporaries struggle with the problem of
motion.

(1) Newton's stated intention in the Scholium is to maintain that
absolute space, time, and motion are genuinely distinct from their
relative counterparts. For the case of space, this clearly amounts to
arguing the existence of an entity distinct from body in which bodies
are located—something denied by relationists. Similarly, for
the case of time, this involves arguing the existence of an entity
distinct from the succession of particular events in which the events
are located—again, something denied by relationists. It may
seem then as a matter of course that, for the case of motion, Newton
should argue for existence of something denied by relationists,
presumably, absolute motion.

(2) It would amount to a virtual petitio principii were
Newton to rest a case for absolute motion on the existence of absolute
space. Hence, one would expect him to appeal to various physical
phenomena that might provide independent warrant. Now it is well known
that Newton's laws satisfy the principle of Galilean relativity,
according to which there can be no experimental test to determine
whether a system is at rest or in a state of uniform rectilinear
motion. However, Newton's laws do support a distinction
between inertial and non-inertial motion in that they predict, in
non-inertial frames, the appearance of so-called “fictitious forces,”
for instance, centrifugal forces in rotating frames, resulting in a
tendency for bodies to recede from the axis of rotation. Since this is
exactly the effect involved in the rotating bucket experiment, it is
tempting to interpret Newton as marshaling it as a case in which this
phenomenon suggests independent warrant for the existence of absolute
motion.

(3) Moreover, since the same effect is operative in the example of
the revolving globes, it is hard to see why that example does not
serve the very same purpose. In fact, in his famous critique of Newton
in the Science of Mechanics, Ernst Mach, in quoting from the
Principia, cut out all of the intervening text to make it
appear as though the two are but variant examples in the development
of a single argument.

(4) Finally, the choice of language in Motte's 1729 translation,
which is the basis for the most widely available twentieth century
English translation by Cajori, tends to reinforce the presumption that
the arguments from properties, causes, and effects seek to identify
phenomena that empirically distinguish absolute from (merely)
apparent motion. In the Cajori version, the conclusions of the first
three arguments, the arguments from the properties of motion and rest,
read:

… it follows that absolute rest cannot be determined from
the position of bodies in our regions.
[Paragraph VIII]

…the true and absolute motion of a body cannot be
determined by the translation of it from those which only seem to
rest;
[Paragraph IX]

Wherefore, entire and absolute motions can be no otherwise
determined than by immovable places;
[Paragraph X]

Thus, it is tempting to assume that both the argument from causes and
the argument from effects are likewise concerned to identify an
empirical signature of absolute motion by which it can be
distinguished from (merely) apparent motion. (Reading the arguments in
this fashion, only the argument from effects, which deals with the
centrifugal effects of circular motion, appears to help Newton's
cause—a commonly registered complaint.)

(Ad 4) It is an artifact of Motte's translation that the Latin verb
definiri (passive infinitive) is rendered occasionally as
‘be determined’ rather than as ‘be
defined’. According to seventeenth-century English usage, either
choice is acceptable. In appropriate contexts, the two function as
synonyms, as in the Euclidean axiom, “Two points determine a line.”
Motte's practice conforms with this. The conclusion of the argument
from effects, ‘definiri’ is translated as ‘be
defined’:

And therefore this endeavor does not
depend upon any translation of the water in respect of the ambient
bodies, nor can true circular motion be defined by such
translation.
[Paragraph XII]

If one now goes back and substitutes ‘be defined’ for
‘be determined’ into the conclusions from the arguments
from properties quoted above, they take on, to the modern ear, a
different meaning. They make claims as to what constitutes an adequate
definition of the concepts of true, or absolute, motion and rest.

(Ad 3) We have already seen how
paragraph XIII
signals the conclusion,
not just of the arguments from properties, causes, and effects, but
the direct arguments for absolute time and absolute space as well,
which, altogether, Newton takes establish the ontological distinction
between the absolute and the relative quantities. That the next
paragraph, in which the globes are introduced, concerns a different,
epistemological issue would be apparent were it not for another
artifact of the Motte translation, this time involving the Latin verb
‘distinguere’. Newton uses the word again and again,
almost thematically, in characterizing and arguing for the ontological
distinction between the absolute and the relative quantities; and
Motte renders it in English as ‘to
distinguish’. Unfortunately, the English verb appears in the
Motte translation one more time at the start of the final paragraph:

It is indeed a matter of great difficulty to discover,
and effectually to distinguish, the true motions of particular bodies
from the apparent;

But in the Latin, the word ‘distinguere’ is nowhere to be
found. Rather, the sentence reads:

Thus, to the Latin reader, it is clear that Newton is moving on to a
different consideration.

(Ad 2) What has been said in connection with (4) suffices against the
false expectations developed in (2). However, there may remain some
sense that, even on a proper reading, Newton tried to bluff his way
past the principle of Galilean relativity. Newton indeed acknowledges
the principle, though not by name, in Corollary V to the laws of
motion:

The motions of bodies in a given [relative] space
are the same among themselves whether that space is at rest or moves
uniformly in a straight line without uniform motion.

And there is no reason to think that he did not appreciate the
limitation it poses for experimentally differentiating between
absolute rest and uniform motion in a straight line. A particular
instance of Corollary V is the solar system as a whole. Assuming the
absence of external forces, it follows (from Corollary IV to the laws)
that the center of gravity of the solar system is either at rest or
moves uniformly in a straight line. But which? Because of Corollary V,
when Newton wishes to attribute a definite state of motion to the
center of mass of the solar system in Book III, he must introduce the
hypothesis that “The center of the system of the world is at
rest.” Should this not be some source of embarrassment?

Apparently not. Immediately following the hypothesis, he writes:

This is conceded by everyone, although some contend it is
the earth, others the sun, that is at rest in the center. Let us see
what follows from this.

According to Newton, the attribution of a state of absolute rest to
one or the other of these bodies is universally taken for
granted. What does confound all conventional wisdom in what follows is
that neither the earth nor the sun is at rest, but rather the
center of gravity of the solar system.

(Ad 1) Although arguing that absolute space and absolute time are
distinct from any relative spaces and relative times involves, in each
case, arguing for the existence of an additional entity, it does not
follow that, in arguing that absolute motion is distinct from relative
motion, Newton is obliged to argue yet another existence
claim. Unfortunately, the term ‘absolute motion’ is prone
to be read in two distinct ways. On one reading, it means, as a matter
of stipulative definition, ‘change of absolute place’. In
this sense of ‘absolute motion’, the existence of absolute
motion (or more precisely, the possibility of the existence of
absolute motion) follows immediately from the existence of absolute
space and absolute time. As indicated before, nothing further needs
to be said. On the other reading, ‘absolute motion’ is
synonymous with ‘true motion’. And as we have just seen,
Newton finds no reason to doubt that his audience does not grant that
a body is either truly at rest or truly in motion. The venerable
tradition that takes motion and rest to be contraries has yet to be
questioned. So it is not incumbent on Newton make a case for the
reality of absolute motion in the sense of true motion. What is
incumbent is for him to argue that true motion just is change of
absolute place. And that is the purpose of the arguments from
properties, causes, and effects.

Newton's views on space, time, and motion dominated physics from the
17th Century until the advent of the theory of relativity in the 20th
Century. Nonetheless, these views have been subjected to frequent
criticism, beginning with contemporaries, such as Leibniz and
Berkeley, and continuing on to the close of the 19th Century, most
notably with Ernst Mach, whose writings influenced Einstein. In the
early twentieth century, Newton tended to be cast as a metaphysical
dogmatist by the early philosophical interpreters of relativity, in
particular Hans Reichenbach. Unfortunately, that stigma has tended to
linger.

More recent scholarship reveals a more sober picture of why Newton
felt fully justified in positing absolute space, absolute time, and
absolute motion. Moreover, the novel feature of special relativity,
the rejection of absolute simultaneity—something that never
occurred to any of Newton's earlier critics—necessitated only
that absolute space and absolute time be replaced with an absolute
space-time (Minkowski spacetime). And although Einstein's development
of general relativity was in large part motivated by a desire to
implement a general principle of relativity, to wit that all motion is
relative motion, that it succeeds in doing so was questioned shortly
after the theory was introduced. As for the question of the
absoluteness of space-time in general relativity, it no longer has the
character of something which acts without being acted upon, as
Einstein himself pointed out. The space-time metric tensor
not only encodes for spatiotemporal structure, but also represents the
gravitational potentials, and thus gravitational energy. By Einstein's
famous equation for the equivalence of energy and mass,
it follows that the gravitational field possesses mass.
Only, since gravitational energy can not be localized in terms of
an energy density tensor, but is possessed by the field holistically,
neither can this mass be localized. Thus, philosophical
controversy as to whether space-time can exist without matter becomes
tendentious according whether one counts the gravitation field as
something material or not.

Thus, the question whether the revolution in our views about space
and time in the last century vindicates Newton's critics as more
philosophically astute becomes a misplaced one. The distinction
between what counts as matter in contrast to empty space presupposed
in the earlier debates has been eclipsed by possibilities undreamt of
before the introduction of modern field
theory and relativity.[1]

Primary Sources

Charleton, Walter, 1654,
Physiologia Epicuro-Gassendo-Charltoniana: or a Fabrick of Science Natural Upon
the Hypothesis of Atoms,
London: Tho. Newcomb.
Reprinted with indices and introduction by Robert Hugh Kargon, New York and London:
Johnson Reprint Corporation, 1966.

Clarke, Samuel, 1717,
A collection of papers, which passed between the late learned Mr. Leibnitz and Dr. Clarke,
in the years 1715 and 1716,
London: J. Knapton.
Reprints:

Grant, E., 1981,
Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution.
Cambridge: Cambridge University Press.

Hall, A. Rupert, 1992,
“Newton and the Absolutes: Sources,”
in The Investigation of Difficult Things: Essays on Newton and the History of the Exact Sciences.
P. M. Harmon and A. Shapiro (eds.), Cambridge: Cambridge University Press, 261–285.

Huggett, N., 2008,
“Why the Parts of Absolute Space are Immobile,”
British Journal for the Philosophy of Science, 59(3): 391–407.

The SEP would like to congratulate the National Endowment for the Humanities on its 50th anniversary and express our indebtedness for the five generous grants it awarded our project from 1997 to 2007.
Readers who have benefited from the SEP are encouraged to examine the NEH’s anniversary page and, if inspired to do so, send a testimonial to neh50@neh.gov.